# Second noble kipiscoidal icositetrahedron

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Second noble kipiscoidal icositetrahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 24 irregular pentagons |

Edges | 12+12+12+12+12 |

Vertices | 24 |

Vertex figure | Irregular pentagon |

Related polytopes | |

Army | Nonuniform snub cube |

Dual | Second noble kisombreroidal icositetrahedron |

Convex core | Non-Catalan pentagonal icositetrahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –12 |

Orientable | No |

Genus | 14 |

Properties | |

Symmetry | B_{3}+, order 24 |

Flag orbits | 10 |

Convex | No |

Nature | Tame |

The **second** **noble kipiscoidal icositetrahedron** is a noble polyhedron. Its 24 congruent faces are irregular pentagons meeting at congruent order-5 vertices. It is a faceting of a non-uniform snub cubic hull.

The ratio between the longest and shortest edges is 1:2.68320.

## Vertex coordinates[edit | edit source]

This polyhedron has coordinates given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of

- (
*1*,*a*,*b*),

where

is the real root of , and

is the real root of .

These are the same coordinates as the noble kipentagrammic icositetrahedron.